ON ELECTROLYSIS IN ITS PHYSICAL AND CHEMICAI, BEARINGS. 359 



2nd. That the conductivity of water itself remains unaffected by the pre- 

 sence of a foreign body ; ■which is improbable.' 



Effect of Dilution. — A great part of the paper is taken up with the effect on 

 conductivity which dilution with an equal quantity of water causes to solutions of 

 various salts. This mode of expression is a roundabout substitute for a straight- 

 forward expression by cui-ve or formula for the relation between conductivity and 

 concentration such as Kohlrausch attempts to give. However, as Dr. Arrhenius 

 evidently prefers this mode of expression, I translate his introduction of it (page 25 

 of his memoir). 



' Table A shows that when a saline solution is diluted in a certain ratio 

 [1 : 6"08, for instance] its conductivity diminishes in a certain other ratio [not in 

 general a very different one]. To render these numbers comparable among them- 

 selves in the different series a recalculation has been made, in which all dilutions 

 are reduced to the ratio 1 : 2. 



' This calculation is made in the following manner. If 1 : m is the proportion 

 between the dilutions of two solutions of the same salt examined consecutively {i.e., 

 if one of the solutions is u times as dilute as the other), the proportion between 

 the resistances in the two cases is, say, 1 : ii (the value of n being taken from the 

 table) ; that is to say, one of the solutions has a conductivity n times less than 

 that of the other. 



' If now 1 : .r is the proportion between the resistances of two solutions when 

 the dilutions are in the proportion 1 : 2, the following relation will hold good. If 

 the dilution is 1 : 2^, the ratio of resistances (if the process is effected in a vmi- 

 form manner) ought to be 1 : .rP. In consequence we have 1 : 2p = 1 : u, and 

 \ : x^ — \ : n, which enables x to be calculated by the following formula : — 

 log log .r = log log n — log log u + log log 2. 



' The values of x calculated from this formida, which, according to what has 

 just been said, signifies the proportion in which the conductivity of one salt- 



(2) The current must divide itself accurately between the two constituents, 

 so that whatever starts to go by one substance must keep to that all 

 the way, and not go partly through one, partly through the other. 

 If these two conditions are not satisfied, the law can only be true in any particular 

 case by some semi-accidental sort of compensation. True there is much to be said 

 for the fulfilment of the second condition in many cases of electrolysis, perhaps in 

 all ; but it cannot be regarded as axiomatic ; and it is certainly not true of inter- 

 mingled conductors in general, which is all I say in the text. The point may be 

 illustrated thus. Take a square sheet of tinfoil, send a current through it between 

 copper strips on its opposite edges, and measure its resistance. Now make an 

 arbitrary cixt across the sheet from one of these edges to the other. The current 

 will divide between the two portions, and the resistance of each portion can be 

 measured. The resistance of the nncvt sheet will not in general be equal to the semi- 

 harmonie mean of the two portions; in other words, the law of divided circuit need 

 not apply. 



It may apply, but only for the special case of a cut along a stream-line. The 

 statement, therefore, that the law of divided circuit mvst hold whenever two con- 

 ductors are intermingled is untrue — Q.E.D. 



As to the question whether the law does hold for any mixed electrolytes we have 

 the experiments of Hittorf and of Buff on the conductivity of mixtures ; with the 

 result, I believe, that whereas all the mixed substances take part in conveying the 

 current, no simple relation holds between the conductivity of the mixture and their 

 separate conductivities except in the case of some haloid salts. For them the law of 

 divided circuits does seem to hold. 



To diminish the risk of misunderstanding, I may be permitted to point out that 

 the remark made in the text is not a criticism of Dr. Arrhenius or of anybodj\ It 

 relates to a general proposition or matter of fact, and is intended as a memorandum 

 of a circumstance which it is very easy to see when pointed out, and rather easy to 

 forget in practice when considering a special case ; cf . Guthrie's Test-book of Elec- 

 tricity, sections 244-247, first edition, w-hich are all wrong in principle as well aa 

 cumbrous in detail. 



' See §§ 2 and 3 of letter on p. 385. 



